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Tr. Mat. Inst. Steklova, 2013, Volume 282, Pages 87–97 (Mi tm3494)  

This article is cited in 4 scientific papers (total in 4 papers)

Multitype subcritical branching processes in a random environment

E. E. Dyakonova

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

Abstract: We investigate a multitype Galton–Watson process in a random environment generated by a sequence of independent identically distributed random variables. Assuming that the mean of the increment $X$ of the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices is negative and the random variable $Xe^X$ has zero mean, we find the asymptotics of the survival probability at time $n$ as $n\to\infty$.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00139
This work was supported by the Russian Foundation for Basic Research, project no. 11-01-00139.


DOI: https://doi.org/10.1134/S0371968513030084

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English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 282, 80–89

Bibliographic databases:

Document Type: Article
UDC: 519.218.27
Received in December 2012

Citation: E. E. Dyakonova, “Multitype subcritical branching processes in a random environment”, Branching processes, random walks, and related problems, Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences, Tr. Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 87–97; Proc. Steklov Inst. Math., 282 (2013), 80–89

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. E. D'yakonova, “Limit theorem for multitype critical branching process evolving in random environment”, Discrete Math. Appl., 25:3 (2015), 137–147  mathnet  crossref  crossref  mathscinet  isi  elib
    2. Elena E. D'yakonova, “Reduced multitype critical branching processes in random environment”, Discrete Math. Appl., 28:1 (2018), 7–22  mathnet  crossref  crossref  mathscinet  isi  elib
    3. N. Bacaer, “On the extinction of populations with several types in a random environment”, C. R. Biol., 341:3 (2018), 145–151  crossref  isi  scopus
    4. V. Vatutin, V. Wachtel, “Multi-type subcritical branching processes in a random environment”, Adv. Appl. Probab., 50:A (2018), 281–289  crossref  mathscinet  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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